Under the condition 100K^2 δ ≤ 1, a set with small doubling and small Fourier coefficients must have a dense intersection with a translate of a large regular Bohr set of controlled dimension.
Uncertainty for convolutions of sets
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The paper obtains the optimal form of the uncertainty principle in the special case of convolution of sets.
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On Fourier coefficients of sets with small doubling
Under the condition 100K^2 δ ≤ 1, a set with small doubling and small Fourier coefficients must have a dense intersection with a translate of a large regular Bohr set of controlled dimension.